Properties

Label 5070.2.b
Level $5070$
Weight $2$
Character orbit 5070.b
Rep. character $\chi_{5070}(1351,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $27$
Sturm bound $2184$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5070.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(2184\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5070, [\chi])\).

Total New Old
Modular forms 1148 100 1048
Cusp forms 1036 100 936
Eisenstein series 112 0 112

Trace form

\( 100 q + 4 q^{3} - 100 q^{4} + 100 q^{9} + O(q^{10}) \) \( 100 q + 4 q^{3} - 100 q^{4} + 100 q^{9} - 4 q^{10} - 4 q^{12} - 8 q^{14} + 100 q^{16} - 8 q^{22} - 100 q^{25} + 4 q^{27} - 16 q^{29} - 4 q^{30} - 8 q^{35} - 100 q^{36} + 32 q^{38} + 4 q^{40} + 8 q^{42} - 16 q^{43} + 4 q^{48} - 52 q^{49} - 8 q^{55} + 8 q^{56} - 40 q^{61} + 16 q^{62} - 100 q^{64} - 8 q^{66} + 16 q^{69} - 8 q^{74} - 4 q^{75} + 80 q^{77} - 16 q^{79} + 100 q^{81} - 16 q^{87} + 8 q^{88} - 4 q^{90} - 32 q^{94} - 32 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5070, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5070.2.b.a 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.b 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.c 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.d 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.e 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.f 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.g 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.h 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.i 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots\)
5070.2.b.j 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.k 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+4iq^{7}+\cdots\)
5070.2.b.l 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+5iq^{7}+\cdots\)
5070.2.b.m 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.n 5070.b 13.b $2$ $40.484$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+2iq^{7}+\cdots\)
5070.2.b.o 5070.b 13.b $4$ $40.484$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}-\zeta_{12}q^{6}+\cdots\)
5070.2.b.p 5070.b 13.b $4$ $40.484$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots\)
5070.2.b.q 5070.b 13.b $4$ $40.484$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{2}+q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{6}+\cdots\)
5070.2.b.r 5070.b 13.b $4$ $40.484$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
5070.2.b.s 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.t 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.u 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.v 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.w 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.x 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.y 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.z 5070.b 13.b $6$ $40.484$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.ba 5070.b 13.b $8$ $40.484$ 8.0.\(\cdots\).1 None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2535, [\chi])\)\(^{\oplus 2}\)